Rules of Exponents
Guided Notes
Algebra Standards:
N.RN.1
Rules of Exponents
N.RN.1
I CAN… rewrite expressions involving rational exponents using the
properties of exponents.
Vocabulary:
Monomial
A number, a variable, or a product of a number and one or more variables
Examples:
Power
52
34xy, 7a2b
Exponent
Base
Rules of Exponents:
Product of Powers:
a m  a n  a m n
If multiplying two numbers with the same base, ADD the exponents
5 2  56
y4  y3  y
(7 y 5 )(6 y)
(3x 2 y 7 )(5xy 6 )
Quotient of Powers:
am
 a mn
an
If dividing two numbers with the same base, SUBTRACT the exponents
y6
y
613
62
10a 7 b 9
15a 5 b 9
Rules of Exponents
Zero Exponent: a
0
1
Any nonzero number with an exponent of zero is equivalent to 1
82
WHY?? Let’s explore 2 ……..
8
8x 0  5
(3x  7) 0
Negative Exponent
a n 
1
an
For any nonzero number “a” raised to a negative exponent, place the
power in the denominator to rewrite the power with a positive
exponent
b2
WHY?? Let’s Explore 5 …….
b
2 3
(3) 3
Rules of Exponents
mn
(a )  a
Power of a Power:
If raising a power to a power, multiply the exponents
m n
Examples: Simplify. Write each answer using only positive exponents:
( y 3 ) 4
(x 2 ) 8
Power of a Product: (ab)  a b
Find the power of each factor in the parenthesis and multiply
m
4 x yz 
3
3
m
6x
7 xy 
 2 2
m
6
y 7 z 0 
2
m
Power of a Quotient:
am
a
   m
b
b
For any numbers “a” and “b” where b  0, if the quotient of a and b is raised to a
power, raise both the numerator and the denominator to the given power
3
 
5
2
 3a 4 
 7 
 b 
 2a 5 
 7 
 b 
3
2
 a  2 b 5 
 11 
 c

6
Rules of Exponents
Thanks for
Shopping!!!
I hope you enjoyed the Rules of Exponents
Guided Notes! You may also enjoy the Rules of
Exponents Reference Sheet or Rules of
Exponents: Different Question/Same Answer
Partner Activity, which are both available in my
store.
Thanks….. Come back soon!!
Elizabeth Kissel 